Two-Period Supply Chain Coordination Strategies with Ambidextrous Sustainable Innovations

This study considers a manufacturer with ambidextrous sustainable innovation capability selling products in environmentally conscious market through an independent retailer in a two-period game setting. We design a two-period game theoretic and dyadic supply chain (SC) model considering exploitative and exploratory nature of environmental innovations. We study five different contract types, viz. wholesale price contract, vertical Nash game structure, cost sharing contract, revenue sharing contract and two-part tariff contract. We demonstrate the impact of market sensitivity towards sustainable innovation and cost parameters on optimal level of decision parameters. The equilibrium results reveal that a suitably designed two-part tariff contract can be used to achieve coordination in a fragmented SC. The equilibrium results assist managers to optimise the SC based on the two-period contract model. The results obtained in this study can help the decision-makers to take decisions on investment in the ambidextrous sustainable innovation under different types of contract structures.


Introduction
Investment in sustainability leads to innovations which yield both net earnings and growth in sales revenue (Nidumolu et al., 2009;Hartmann and Vachon, 2018;Hizarci-Payne et al., 2021). The sustainability is being viewed as a source of innovation and new growth among business managers (KPMG, 2017;Wicki and Hansen, 2019;Wang, 2020). The extant literature discusses two basic forms of innovation that enhances the environmental performance, viz., exploratory and exploitative (Gibson and Birkinshaw, 2004;Awan et al., 2021). A business organisation that pursues exploitative (continuous) innovation builds on existing knowledge, whereas an organisation that pursues exploratory (disruptive) innovation relies on radical change built on new knowledge (Kim and Huh, 2015). The new knowledge thorough exploratory innovation could be regarding the development of more sustainable new product and services for existing customers, or developing product for new segments.
For example, Abbott Laboratories is a medical devices and healthcare company that has achieved a high growth through disruptive innovations in medical devices and diagnostics and opened up several new markets in developing countries (Ahlstrom, 2010).
Through exploitative innovations, business organisations continuously strive to improve their existing products, processes and technologies. Proponent of this strategy for sustainability argues that it is based on addressing environmental and social issues thereby contributing to profit maximisation (Hosseini-Motlagh et al., 2019;Phan et al., 2019;Raza, 2018). For instance, GM's Flint plant in Michigan is saving approximately 174,299 kWh energy per year by shutting down plant during holidays (El Bizat, 2006). Instead of venting to the atmosphere, Statoil injects more than 1 million tonnes of CO2 per year underneath the North Sea bed to save paying carbon tax to Norway (Stefan and Paul, 2008).
The gains from the exploratory innovations are not immediate. The exploratory innovations require concentrated efforts for a longer time periods and may not result in direct visible savings in the same time period when we invest into it. A lot of disruptive sustainable innovations have brought additional purchasers into the markets earlier who could not consume or meet the expense of the conventional product (Christensen and Raynor, 2003;Jakhar et al., 2020).
A firm engaging in both innovation strategies as discussed above is termed as ambidextrous (Lin et al., 2017). The recent development of ambidexterity stems from the recognition that exploration engenders prospects that an organisation can later exploit (Kim and Atuahene-Gima, 2010;Lavie et al., 2010;Mueller et al., 2013). Gupta et al. (2006) discussed ambidextrous innovative behaviour of Cisco and other firms in the semiconductor industry. Knott (2002) observed that exploration and exploitation coexisted in Toyota's product development system. The Toyota Fuel Cell System is an excellent example that includes both fuel cell technology and hybrid technology based ambidextrous sustainability innovation practices.
There are three ways to measure ambidextrous innovations as subtracting (He and Wong, 2004), multiplying (Gibson and Birkinshaw, 2004), and adding (Jansen et al., 2006(Jansen et al., , 2009Kortmann et al., 2014) of exploratory and exploitative innovations. However, it has been proved that the additive model possesses greater explanatory power as compared to the other two approaches (see Jansen et al., 2009, p. 803 for a detailed analysis).

Research questions and goals
Motivated by the above background where the firms invest in the exploratory and exploitative innovation, we propose that environmental innovation has a two-pronged impact: (i) reduction in cost due to eco-efficiency and (ii) the expansion of emerging markets (e.g., the bottom of the pyramid). Moreover, investment in sustainability will cause an increase in demand due to environmentally conscious buyers in the existing markets ( Figure   1).
The extant literature considers environmental innovation in various models (Hong and Guo, 2019;Shen et al., 2019;Xie et al., 2019;Nguyen et al., 2020). In sustainability literature, these two strategies are known as eco-efficiency and eco-branding, respectively (Orsato, 2006). Whereas the competitive focus of eco-efficiency strategy is on a manufacturing/service process, the competitive focus of eco-branding strategy is on the output of a manufacturing/service process. It is fundamental to recognize that focusing on eco-efficiency is not equivalent to focusing on eco-branding (or vice versa). One strategy is about reducing the environmental impact of a product during its manufacturing stage (e.g., using renewable energy sources to power the manufacturing plant, reducing water usage during the production process), whereas the other is about reducing the environmental impact of a product during its use stage (e.g., increasing the energy efficiency of a washer unit). Raz et al. (2013) examine a firm's design for the environment efforts that change the product's environmental impacts in each life-cycle stage and therefore its overall environmental impact. In their model, the cost to produce the product is decreasing in the innovation effort for the manufacturing stage (i.e. exploitative innovation), whereas endcustomer demand is stochastic and depends on the use stage innovation effort (i.e., exploratory innovation). However, the most of literature overlooks the exploratory and exploitative nature of environmental innovation. This study takes breakthrough step and considers ambidextrous nature of sustainable innovation, and demonstrates the effectiveness of the two-period contract structure. Although some two-period contract models are available in literature (Chakraborty et al., 2019;Hartwig et al., 2015;Merckx and Chaturvedi, 2020;Pan et al., 2009), they do not consider exploratory and exploitative nature of environmental innovation. Driven by the above discussion the following research questions are posed: • How an analytical model can be formed by simultaneously considering exploratory and exploitative nature of environmental innovation?
• In a dyadic supply chain, how does the decision maker's investment in environmental innovation influence the measures of supply chain performance? And, in which contract structure, the supply chain performance is better?
• What are the changes in optimal level of decision parameters of a two-period contract model considering ambidextrous nature of sustainable innovation?
• What is the impact of market sensitivity towards environmental innovation and its cost parameters on the measures of supply chain performance in a two-period contract setting?
• What is the impact of exploratory and exploitative nature of environmental innovation on the measures of supply chain performance in a two-period contract setting?
To address these questions, we design a two-period game theoretic and dyadic supply chain model considering simultaneously exploitative and exploratory nature of environmental innovations. The manufacturer, assumed to be a Stackelberg leader, invests in ambidextrous sustainable innovations. We discuss five different contract types, viz. wholesale price contract (WSP), vertical Nash game structure(VN), cost sharing contract (CSC), revenue sharing contract (RSC), and two-part tariff contract (2PT). First, we study wholesale price contract. As this contract structure leads to sub-optimal solution failing to coordinate the supply chain, we discuss vertical Nash game structure relaxing the assumption of Stackelberg structure.
Subsequently, we consider other three different contracts, viz. CSC, RSC and 2PT.  Figure 1: Impact of environmental investment

Research contribution
This study contributes to the literature in multiple ways. Firstly, we develop a two-period contract setting with ambidextrous sustainable innovations. Second, we study a two-period game using five different contract types and delineate its effectiveness using numerical examples. Third, we discuss the nature of changes in the level of optimal value of decision parameters in ambidextrous sustainable innovation based on the two-period contract setting.
Fourth, we analyse the impact of consumer sensitivity of sustainable innovation and sustainable cost parameter on the decision parameters of the two-period contract models.
Fifth, we analyse the impact of exploratory and exploitative nature of environmental innovation in the two-period contract setting.

Knowledge gaps
The literature limits their analysis to supply chain coordination while considering the trade-off between "cost of sustainability" and increase in demand due to "environmental conscious Moreover, the extant literature on coordination mechanisms and strategies with sustainability also assumes that the sustainable innovation does not change the marginal cost of manufacturers. We deviate from the extant literature by proposing that the supply chains invest in sustainable products and technology not only to satisfy environmentally conscious consumers but also to reduce material/production costs and to develop new markets. We consider two possible scenarios for investment in sustainable innovation, viz. (i) exploitative sustainable innovation and (ii) exploratory innovation. The exploitative sustainable innovation makes existing products more sustainable by reducing the consumption of material and energy. The resultant impact is cost saving (e.g. through low cost of production). The exploratory innovation develops new products and markets which will come with a time lag as exploration takes time. In this article we consider one period time lag.
This article attempts to address these knowledge gaps by considering two types of sustainable innovation in a two-period setting. We explain a game theoretic model for supply chain coordination (Cachon, 2003;Chen and Nie, 2020), and demonstrate the impact of sustainable innovation on demand and cost of a product. The game theoretic method is extensively used in literature to analyse the interaction between two or more players (Yazan et al., 2020). In this context, we analyse four contracts, viz. WSP, RSC, CSC and linear 2PT contract using non-cooperative game theory.
The remainder of the paper is organised as follows. The study model, its assumptions, and game constructs are presented in section 2. Section 3 details the results of the analysis.
Finally, section 4 elucidates conclusions and future research direction.

The Model
Consider a dyadic supply chain (SC) consisting of a manufacturer and retailer ( Figure 2).
The manufacturer supplies only one type of product while the retailer sells that product.
Both the supply chain partners are considered to be individually rational (voluntary participation) and risk neutral (linear utility function) in nature. The manufacturer and retailer are assumed to be the Stackelberg leader and follower respectively. Consumers are sensitive towards environmental issues. The manufacturer performs incremental and radical in-nature sustainable innovations. For the radical innovation, the market potential of period (t+1) is linearly dependent on sustainable innovation level of period t (Christensen and Raynor, 2003), thus +1 = + . With incremental innovation, the manufacturer improves its processes and becomes more efficient which results in reduction of production cost in the second period (Sharma and Henriques, 2005) which is expressed as: +1 = − . The linear, deterministic demand function with negative and positive correlation with price and sustainable innovation level is considered in our study as: Similar demand function is used in previous studies on single period contract models (Swami and Shah, 2013).
The selling price consists cost plus profit margin (Choi, 1991). Mathematically, = + . The cost of sustainable innovation is supposed to be the quadratic function of level of sustainable innovation (Swami and Shah, 2013), which is = 2 . Table 1 provides the notations used in this model.

Centralised supply chain
In the 'coordination' literature, the centralised case provides benchmark solution. In the centralised SC, the owner decides the level of sustainable innovation ( 1 2 ), retail prices ( 1 2 ), and order quantity ( 1 2 ). In the first period, the chain owner fixes the level of retail price ( 1 ) and sustainable innovation ( 1 ). Similarly, in the second period, the chain owner fixes the level of retail price ( 2 ) and sustainable innovation ( 2 ). The backward induction method is used to derive the optimal decision parameters of the twoperiod model. In this case, first of all, the equilibrium level of decision parameters ( 2 2 ) of the second period are derived and then, based on results of second period, the equilibrium level of decision parameters ( 1 1 ) of the first period are derived. In case of the centralised SC, the profit function is jointly concave in ( , ) when ( 4 − 2 ) > 2( + )√ . The equilibrium results for the centralised SC are illustrated in Table 2. The steps of proof of equilibrium results are provided in Table A of Appendix and derivations are given in online supplementary material. Market potential in period 2 Consumer sensitivity to price 3 Per unit variable cost of manufacturer in period 4 Consumer sensitivity to sustainable innovation 5 Cost reduction coefficient due to sustainable innovation 6 Market development coefficient due to sustainable innovation 7 Sustainable innovation level in period 8 Cost parameter of sustainable innovation I 9 Margin of retailer in period 10 Wholesale price of manufacturer in period 11 Retail price in period 12 Demand in period t 13 Aggregate profit of the manufacturer 14 Aggregate profit of the retailer 15 Aggregate profit of the supply chain 16 Manufacturer's profit in period 1 and 2 1 2

18
Supply chain profit in period 1 and 2 1 2

19
Vertical Nash game VN 20 Centralised decision making CENT Note: For the first period, and is used in the place of 1 and 1 respectively, i.e. Market potential of first period( ) and 1 is used interchangeably.
Figure 2: The model

Vertical Nash game
The vertical Nash game structure assumes that all the SC agents have similar market power.
In the initial period, the retailer decides 1 and the manufacturer decides 1 and 1 simultaneously. Based on the response function of the initial period, in the second period, the retailer decides 2 and the manufacturer decides 2 and 2 simultaneously. The backward induction method is used to compute the optimal decision parameters of the vertical Nash game in the two-period model. In this scenario, first the equilibrium results for the second period are derived. Then based on the response functions of the second period, the equilibrium results of first period are derived. In other words, in the second period, the retailer decides 2 and the manufacturer decides 2 and 2 simultaneously. After getting the results of the second period, the retailer decides 1 and the manufacturer decides 1 and 1 simultaneously in the first period. The equilibrium results for the vertical Nash game are presented in Table 2. The steps of proof of equilibrium results are provided in Table A of Appendix and derivations are given in the online supplementary material.

Wholesale price contract
In the scenario, the manufacturer is considered as the market leader in the Stackelberg game while the retailer is considered as a follower. In the first period, based on the response function of the retailer, the manufacturer sets the wholesale price ( 1 ) and level of sustainable innovation ( 1 ). Then the retailer decides their profit margin ( 1 ) using the values of 1 and 1 . Similarly, in the second period, based on the response function of the retailer, the manufacturer sets the wholesale price ( 2 ) and level of sustainable innovation ( 2 ). The retailer decides their profit margin ( 2 ) using the level of 2 and 2 . The equilibrium results for the second period are derived using the backward induction method, and then, based on the response functions of the second period, the equilibrium results for first period are derived. Similarly, in the first period, based on the response function of second period, the retailer decides their profit margin ( 1 ). Finally, in the last stage of the game, the manufacturer decides their level of wholesale price ( 1 ) and sustainable innovation ( 1 ) depending on the profit margin of the retailer ( 1 ). The equilibrium results for the two-period WSP contract are presented in Table 2. The steps of proof of equilibrium results are provided in Table A of Appendix. Derivations are given in the online supplementary material.

Cost sharing contract
In this contract, the retailer contributes a portion of the total cost of the sustainable innovation and if the manufacturer agrees to the offer, remaining fraction of sustainable innovation cost is borne by them. Due to sharing of cost by the retailer, the manufacturer can be motivated for sustainable performance. In the first period, first of all the retailer contributes 1 fraction of the total cost of sustainability, and given the level of cost sharing fraction by the retailer, the manufacturer decides 1 and 1 . The retailer decides their profit margin ( 1 ) considering 1 , 1 , and 1 . Similarly, in the second period, the retailer shares 2 fraction of the total cost of sustainability. Then with the given level of cost sharing by the retailer, the manufacturer decides 2 and 2 . The retailer decides their profit margin ( 2 ) considering the level of 2 , 2 , and 2 . Similar to the vertical Nash game and WSP contract, the backward induction method is used to compute the equilibrium results for the CSC. The equilibrium results for the second period are derived followed by the solution of the equilibrium results for the first period. The equilibrium results of the two-period CSC are presented in Table 2. The steps of proof of equilibrium results are provided in Table A of Appendix and derivations are given in the online supplementary material.

Revenue sharing contract
In this contract type, the retailer contributes a fraction of their revenue with the manufacturer to motivate the manufacturer to decrease the wholesale price, or increase the level of sustainability, or both. In the beginning of the first period, the retailer offers to share (1 − 1 ) fraction of revenue with the manufacturer. The retailer decides the level of the wholesale price ( 1 ) and sustainable innovation ( 1 ) if the manufacturer decides to accept the offer. Finally, the retailer decides their profit margin ( 1 ) considering the level of 1 , 1 and 1 . Similarly, in the second period, considering the response function of the first period, the retailer offers to share (1 − 2 ) fraction of revenue with the manufacturer. If the manufacturer accepts the offer, the retailer decides the level of 2 and 2 . Finally, the retailer decides their profit margin ( 2 ) considering the levels of 2 , 2 and 2 . Similar to vertical Nash game, WSP and CSC, the backward induction method is applied to compute the equilibrium results of the two-period RSC. The equilibrium results of two-period RSC are presented in Table 2. The steps of proof of equilibrium results are provided in Table A of Appendix and derivations are given in the online supplementary material.

Two-part tariff contract
A linear two-part tariff (2PT) contract is considered where the manufacturer sets a lump-sum payment, level of sustainable innovation and wholesale price. From the level of lump-sum payment, sustainable innovation and wholesale price, the retailer decides the retail price. In the first period the manufacturer decides the lump-sum fee ( 1 ), level of sustainable innovation ( 1 ), and wholesale price ( 1 ), and then the retailer fixes their profit margin ( 1 ) considering the levels of 1 , 1 , and 1 . Similarly, in the second period, the manufacturer decides 2 , 2 and 2 , and the retailer decides their profit margin ( 2 ) considering the levels of 2 , 2 and 2 . The backward induction method is applied to compute the equilibrium results of the two-period linear 2PT contract. In the first period, the retailer arrives at 1 considering the response functions of the first period and the response function of the manufacturer. At the end of the event, after considering the decision of the retailer on their profit margin ( 1 ), the manufacturer decides 1 , 1 and 1 . The equilibrium results of the two-period 2PT contract are presented in Table 2. The steps of proof of equilibrium results are provided in Table A of Appendix, and derivations are given in the online supplementary material.

Results and Discussion
This section presents the propositions derived through algebraic comparisons. The proofs of all the propositions are given in the online supplementary material. A numerical analysis is performed to compare the optimal results obtained for different contract types. Finally, the sensitivity analysis of the results is presented.
Proposition 1: In case of the two-period contract, the optimal level of the retail price follows the following order: Proposition 1 demonstrates that for the WSP contract, the optimal level of retail price is higher in the second period than that of the first period. The same is the case for the 2PT contract and centralised SC. This proposition further demonstrates that in case of the 2PT contract, the optimal level of the retail price can be equated with the centralised SC. The reason for the same is that the one-time payment becomes sunk cost and the 2PT contract SC behaves like a centralised SC.
Proposition 2: In case of the two-period contract, the optimal levels of sustainable innovation are in order of: Proposition 2 demonstrates that for the WSP, 2PT, CSC and vertical Nash game, the optimal level of sustainable innovation is less in the second period than the period one. The reason is the time lag for the benefit due to exploratory innovation. No future period is attached to the second period. Moreover, the other explanation could be diminishing marginal return as the low hanging fruits are plucked in the first period. This proposition further demonstrates that in the 2PT contract, the optimal level of the sustainable innovation can be equated to the optimal level of the sustainable innovation in the centralised SC for both the periods.
Proposition 3: For the two-period contract, the equilibrium level of the order quantity follows the following order: Proposition 3 demonstrates that in the case of the WSP, 2PT contract, and vertical Nash game, the optimal level of the order quantity is higher in the second period than the optimal level of the order quantity in the first period. The increase in the order size is due to an increase in market size because of the radical innovations. This proposition further illustrates that for the 2PT contract, the optimal level of order quantity can be equated to the optimal level of order quantity in the centralised SC in both the periods.
Proposition 4 demonstrates that in case of the WSP contract, the optimal level of the profit of the retailer is higher in the second period than the optimal level of the profit of the retailer in the first period. The retailer is benefited by an increase in the market size which reflects an increase in the profit of the second period. However, the benefit of the cost reduction may not be transferred to the retailer by the manufacturer as we can see in Proposition 1 that retail price is higher in the second period. This proposition further exhibits that the optimal level of the profit for the retailer is same in both the periods in 2PT contract.
This is due to the fact that the manufacturer may be barging for higher upfront payment in the second period as they are investing for the sustainable innovation. Moreover, the manufacturer only invests in the sustainable innovations. The following section presents numerical simulation results and graphical analysis to study the impacts of model parameters on the equilibrium results in different channel structures. The following parameter values are considered in our study: 1 = 500, 1 = 20, = 8.5 10.5, = 2.5 4, = 1 2.4, = 0 0.7, and ̅ = 100000.   Table 2 are given in Appendix A.1.

Effect of consumer sensitivity to sustainable innovation
The numerical parameter values for the analysis in this section are chosen in a way to satisfy the conditions of profit function concavity, along with demand functions positivity (conditions are provided in the online supplementary material) and satisfy the assumptions of model. It is observed from Figures 3 and 4 that consumer sensitivity to the sustainable innovation ( ) has increasing impact on sustainable innovation level ( ) (Figure 3a), retail price ( ) (Figure 3b), order quantity ( ) (Figure 4(a)), and profit of retailer ( ) ( Figure   4(b)). However, the rate of increase is different for different contract types. Further, the consumer sensitivity to the sustainable innovation has mixed impact on the profit of the manufacturer (Figures 5(a) and 5(b)). In the first period, the profit of the manufacturer ( ) decreases with the increase in consumer sensitivity to the sustainable innovation for the cases of vertical Nash game and CSC. However, for the WSP and RSC, first it increases then decreases with the increase in consumer sensitivity to the sustainable innovation ( Figure 5(a)). In the second period, increases with the increase in . For a 2PT contract, the decreases in the first period whereas it increases in the second period ( Figure 5(a)).
The aggregate profit of the manufacturer, retailer and total supply increases with an increase in consumer sensitivity to the sustainable innovation. These interesting results provide a justification regarding why there is a need to analyse contracts for sustainability for multiple time periods. Furthermore, it also provides a key guidance to the SC managers regarding how the manufacturer is going to behave with respect to deciding investment level for the sustainable innovations. For example, for the WSP and RSC, there is an optimal investment level for a given customer sensitivity level of sustainable. Moreover, for the vertical Nash, CSC and 2PT contract, the manufacture should consider both the periods together for deciding the optimal investment level. If the manufacturer considers only a single period, then the investment is going to be lowered as compared with both the periods. These results justify the needs to consider multi-period setting while analysing the level of sustainability by the manufacture in different contract types. The optimal level of sustainable innovation ( ) is the highest in the 2PT contract and centralised supply chain (CENT) and it is the lowest in the WSP (Figure 3(a)). The lower level of sustainable innovation for some contracts (e.g. WSP) is due to the problem of double marginalisation and externality. The cost for sustainability is absorbed by the manufacture but benefits are shared with the retailer specifically for increase in the market size. However, in case of the 2PT contract the manufacture may barging for higher upfront fee for the second period that repay cost incurred and the resultant benefit of the sustainable innovation. As shown in Figure 3(b), the retail price is higher in the second period as compared with the first period for all cases, viz. CENT, 2PT, RSC, CSC, vertical Nash game, and WSP contract. The lower level of price in the first period can help to attract the customer in the first period, however the increased market size due to radical sustainable innovation can help the retailer to charge more in the second period. The analysis also suggests that as the level of sustainability increases, product becomes more costlier (Paparoidamis et al., 2019).

Figure 3: Impact of
From Figure 4(a), it is observed that the order quantity (equivalent to the demand) of the product is higher in the second period as compared with the demand in the first period. Figure   4(a) also illustrates that the order quantity is highest in the CENT and 2PT contract, and it is the lowest in the WSP contract. In the WSP contract the retailer pays same amount for every unit purchased from the manufacturer where the expected profit (i.e. price × probability to able to sell) goes down and the retailer ends up ordering less units.
It is apparent from Figure 4(b) that in case of the 2PT contract, the profit of the retailer is independent of the change in consumer sensitivity of the sustainable innovation ( ), while it shows an increasing trend in case of the RSC, CSC, WSP contract, and vertical Nash game structure. The profit of the retailer is higher in the second period as compared with the profit in the first period ( Figure 5(b)) in case of the RSC, CSC, WSP contract, and vertical Nash game structure. In case of the 2PT contract, the profit of the retailer is same in both the periods. the is higher in the second period as compared with the first period. The reason behind this is the reduction of the cost due to exploratory innovations and increase in market size due to exploitative innovations. We also observe that the is the highest in the 2PT and RSC contracts and the lowest in the vertical Nash game structure. Moreover, the behaves differently in both the periods. The profit decreases in the first period and increases in the second period. The reason behind this is that as the consumer sensitivity towards sustainable products increases, the manufacturer invests more in sustainable innovations. This results in more upfront investment in period 1 which decreases it profitability in the same period.
However, it results in more profitability in longer run as reflected in profit in second periods.
These results indicate that the manufacture needs to account long term profitability while investing in the sustainable innovations. The short-term profitability orientation may not provide true potential of the sustainable investment. settings. Similar to the previous case (Figure 3(a)), the optimal level of sustainable innovation is lower in the second period as compared with the optimal level of sustainable innovation in the first period. Furthermore, the increasing impact of on the optimal level of sustainable innovation ( ) is higher in the CENT and 2PT contract as compared to RSC, CSC, WSP contract and vertical Nash game. We also find that difference between the sustainable innovation level of the first and second period is lower at a lower level of cost reduction coefficient as compared with the higher values of the cost reduction coefficient. Figure 6(b) highlights an interesting relationship between the cost reduction coefficient ( ) and retail price ( ). The has increasing impact on the retail price. Figure 6(b) also elucidates that in case of CENT, 2PT contract, CSC, WSP contract, and vertical Nash game, the difference between the retail price of the first and second periods is higher at the lower level cost reduction coefficient as compared with the higher level of the cost reduction coefficient.
We get opposite result in case of the RSC. In case of the RSC, the difference between the retail price of the second and first periods is lower at the lower level of as compared with the higher level of .
As shown in Figure 7(a), the cost reduction coefficient ( ) has an increasing impact on the demand or order quantity of the product in both periods of the contracts. In case of the CENT, 2PT contract, CSC, WSP contract and vertical Nash game, the order quantity of the second period is higher than the order quantity of the first period. We get the opposite result in case of the RSC, in which the order quantity of the first period is higher than the order quantity of the second period. In case of the CENT and 2PT contract, CSC, WSP contract and vertical Nash game, the difference between the order quantity of the second and first periods is lower at the lower level of the cost reduction coefficient as compared with the higher level of the coefficient. For the RSC the difference between order quantity of the first and second periods is lower at the lower level of the cost reduction coefficient. The value of has a mixed impact on . In the first period of the contract, the profit decreases with an increase in the cost reduction coefficient, while in the second period, the profit increases with an increase in the cost reduction coefficient. Figure 7(b) also illustrates that the difference between the value of in the second and first periods increases with respect to an increase in the cost reduction coefficient.
As shown in Figure 7(c), the cost reduction coefficient ( ) has a mixed impact on the optimal profit level of the retailer. The has a non-decreasing impact on the difference between the second and first periods profit level of the retailer. In case of the 2PT contract, the retailer's profit is same in both the contract periods.
In case of the RSC, CSC, WSP contract and vertical Nash game, the optimal profit level of the second period is higher than that of the first period. In case of the first period of the RSC and CSC, the optimal level of the retailer's profit increases and then it decreases after a certain level of the coefficient.  (Figure 8). The reason behind this is that the costlier sustainable innovation becomes less attractive for the manufacturer to invest, which results in less demand from the sustainable sensitive customers. So, the retailer reduces the price to attract more customers.
The rate of decrease is the highest for 2PT contract as the retailer paid upfront initial cost and needs more customer to recover the initial investment.
The order quantity (Figure 8(b)) also decreases with an increase in the cost parameter of the sustainable innovation. The reason is the decrease in demand due to less investment in the sustainable innovations from the manufacturer. The profit of the manufacturer ( Figure   9(a)) decreases in the second period with an increase in the cost parameter of the sustainable innovation. The rate of decrease is the highest for the RSC. On the contrary there is a slight increase in the manufacturer's profit for the first period. Due to the high cost for the sustainable innovation, the manufacturer tends to invest less and save some initial investment cost in the first period. However, this leads to significant reduction in the manufacturer's profit in the second period. The profit of the retailer (Figure 9(b)) also shows the same pattern as that of the manufacturer. Nash as compared with the RSC when the market with development coefficient value is less than 1.8. However, the retailer earns more profit in the RSC when the market development coefficient value is greater than 1.8. These results provide valuable guidance to the retailer on the type of contract that maximises its profit for a given value of . innovations on the measures of supply chain performance using five different two-period game structures, viz. wholesale price contract, vertical Nash game, cost sharing contract, revenue sharing contract, and two-part tariff contract. The study compares the results of period one and period two, and discusses the nature of changes in the optimal level of decision parameters. Further, the study demonstrates the impact of market sensitivity towards sustainable innovation and its cost parameter on optimal level of decision parameters of the two-period models. Finally, this study investigates the impacts of exploratory and exploitative nature of innovation on the decision parameters of the twoperiod contract models. The results demonstrate that a suitably designed 2PT contract can be used for coordination of a decentralised supply chain. A sensitivity analysis is performed for sustainability cost parameter, consumer sensitivity to sustainable innovation and cost reduction coefficient.
Based on the analysis of the results, we submit that in ongoing business relationships, the promise of future rewards, may provide incentives for good behaviour today. Here we refer the 'good behaviour' as 'environmentally responsible manufacturing'. Some gains from the investment in sustainable innovations are noticed after a time lag, particularly for the case of exploratory innovations. This provides justification for considering multi-period setting for the supply chain coordination using the sustainable investment. Furthermore, the study reveals that the investment in sustainable innovation is significantly lower in the second period. There is no future period available to receive benefits of the investment in this period and the manufacture invests less in this period. Therefore, we propose that consideration of long-term gain perspective can incentivize the manufacturer to put their investment more in the sustainable innovations. Moreover, as the innovation literature agrees that for the exploratory innovations, the fruits can only be reaped after a time lag. By considering only a single period setting, the manufacture may not be willing to invest in the exploratory sustainable innovations. By considering a two period setting, the long term perspective for sustainability is incorporated in our model. The manufacturer may be willing to invest in exploratory sustainable innovations to reap long term benefits. We believe that this is the first study to incorporate the two period setting for ambidextrous sustainable innovation.  The equilibrium results presented in Table 2 can help managers to optimise the supply chain based on the two-period contract model. it is found to increase with an increase in . has non-decreasing impact on difference between the second period and first period profit of the retailer.